"At least 18 people died and around 30 were injured," the governor, Major General Clement Wani, said on Wednesday.
Aid workers in the town said that judging by the extensive damage they thought the toll would be much higher.
"It's a bloody mess. There are bodies that have been burnt to nothing. There's unexploded ordnance everywhere and almost half of the city has been blown up," said one aid worker, who asked not to be named.
"It looks like a war zone," said another aid worker, who also asked not to be named. "Shells were falling within an area 4km in diameter," she added.
Gemma Mortensen, a British journalist who happened to be visiting the town, said: "The sky just ignited and shells started firing themselves."
An unexploded anti-aircraft missile 2m long landed outside the compound of the UN Children's Fund Unicef, she added.
One of the aid workers quoted witnesses as saying they had seen between 15 and 20 bodies.
"It looks like a war zone. Shells were falling within an area 4km in diameter"
The explosion took place in the area known as the customs market in the west of the town and houses were destroyed or burnt all the way to the town centre, she added.
The Sudan Radio Service, a US-funded station based in the Kenyan capital Nairobi and broadcasting to southern Sudan, said houses in the area were burnt to ashes and some shells fell in the nearby offices of a charity organisation.
Throughout more than two decades of civil war in southern Sudan, Juba remained in government hands, with a large military presence to protect it from rebels.
The government and the rebel Sudan People's Liberation Movement signed a peace agreement in Nairobi in January.
Mortensen said army officers were speculating that the
ammunition dump ignited accidentally because of a recent spell of hot weather and because of poor storage methods.